The difference here is semantic rather than grammatical. I mean, "from" is there to identify the specific meaning of "come" in context. It is not required for a grammatical reason related to the sentence pattern itself.
As you probably know, "come" is a versatile word with a lot of meanings, depending on the preposition. In addition to:
- Where do you come from?
You can also have:
- Where do you come out? [If you crawl into this tunnel, where will you be when you emerge?]
- Where did he come across the body? [Where was he when he found the body?]
- Where does this road come through? [There are lots of roads in this forest and I want to know where this one exits the forest]
- Where did he come into his fortune? [Did he get rich on a trading voyage to India?]
- Where do you come? [Note: "come" with no preposition can, in some contexts, mean 'reach sexual climax'. This sentence is grammatical and would be understood, but probably is not what you want to say!]
"From" is there because "to come from" a place is different from "to come to" a place, or any of the other variations above.
For your second question, the sentence patterns:
- When can you [verb]
- What time will you [verb]
do not usually require a preposition. (Also "come" in these sentences, without a preposition and without some other context, would be understood to mean either "arrive at my location" or "attend a social event"--no worries about innuendo there).
You will see speakers of certain American dialects use "at" at the end of those patterns, like "What time will you come at?" This is casual, nonstandard phrasing; it's preferred not to use it in formal standard American English. (It's just the speaker taking the "at" from the expected reply--"I will come at 11"--and putting it on the question.)